This week we took a practice AP test which consisted of four parts. I"m quite amazed that i did better on the free response than the multiple choice. I'll start by going over some easy concepts:
First derivative test:
You have to take the derivative of the function and then set it equal to zero. Then solve for the x intercepts (critical points). After that, set the intercepts up into intervals between negative infinity and infinity. Plug in a number between those intervals to find max or mins, or if the graph is increasing or decreasing.
Second derivative test:
You take the derivative of the function twice and set equal to zero. Solve for the x intercepts once more and set them up into intervals between negative infinity and infinity. Plug in values between those intervals into the second derivative to find if the graph is concave up, concave down, or where there is a point of inflection.
Tangent lines:
You will be given a function and an x intercept. If no y intercept is given, plug the x value into the original function and solve for y. Then take the derivative of the function and plug in the x value to find the slope. Then put everything into point-slope form y-y1=slope(x-x1).
Limit rules:
If the degree on top is smaller than the degree on the bottom, the limit is zero
If the degree on top is bigger than the degree on the bottom, the limit is infinity.
If the degree on top is the same as the degree on the bottom, divide the coefficients and that will be the limit
Things i struggle with:
complicated integrals (such as ones that u have to use trig identities for)
Related Rates
Optimization
I hope you all have a great week :)
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RELATED RATES:
ReplyDeletethese are the steps:
1. Identify all of the variables and equations
2. Identify the things that you are looking for
3. Sketch a graph and then label that graph
4. Create and write an equation using all of the variables
5. Take the derivative of this equation with respect to time
6. Substitute everything back in
7. Solve the equation
HOPE THIS HELPS
the related steps are easy. identify the equations and variables then you look for everything u must find. sketch a graph and label it then write an eqn using the variables take the der of that w/ respect to time and substitue everything back in and solve it.
ReplyDeleteOPTIMIZATION!:
ReplyDelete1. Identify primary and secondary equations. Primary deals with the variable that is being maximized or minimized. The secondary equation is the other one.
2. Solve the secondary equation for one variable
3. Plug ^that variable back into the primary. If the primary equation only has one variable you can skip this step.
4. Take the derivative of the primary equation after plugging in the variable
5. Set it equal to zero and solve.
6. Plug that variable back into the secondary equation in order to solve for the last missing variable.
Steps for related rates:
ReplyDelete1. Identify all of the variables and equations
2. Identify the things that you are looking for
3. Sketch a graph and then label that graph
4. Create and write an equation using all of the variables
5. Take the derivative of this equation with respect to time
6. Substitute everything back in
7. Solve the equation
I have a lot of trouble with related rates and i know just saying these steps might not help, but really disect them and it's worth a try :)
1: identify all variables in equations
ReplyDelete2: identify what you are looking for
3: sketch and label
4: write an equation involving your variables. (you can only have one unknown so a secondary equation may be given)
5: take the derivative with respect to time.
6: substitute derivative and solve.
here's some steps for related rates
ReplyDelete1: identify all variables in equations
2: identify what you are looking for
3: sketch and label
4: write an equation involving your variables. (you can only have one unknown so a secondary equation may be given)
5: take the derivative with respect to time.
6: substitute derivative and solve.